Multi-layer anti-reflection coatings using intermediate layers having monotonically graded refractive index

ABSTRACT

An anti-reflection multiple layer coating is formed on a transparent substrate by successive deposition of an inner layer, at least three intermediate layers and an outer layer, the optical thicknesses of the inner and outer layers being approximately lambda /4 and the overall optical thickness of the coating being approximately lambda , where lambda is a reference wavelength within the band of wavelengths over which reflection is to be reduced. The intermediate layers are formed with progressively decreasing refractive indices from the innermost to the outermost intermediate layers, either as a number of separate layers or as a single layer of graded refractive index.

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F awcett et al. 1 Dec. 19, 1972 7 I54) MULTI-LAYER ANTI-REFLECTION OTHER PUBLICATIONS COATINGS USING INTERMEDIATE Strong, 1.; Practical Applications of High and LAYERS HAVING MONOTONICALLY Low-Reflecting Films on Glass" Journal de Physique GRADE REFRACTIVE INDEX et le Radium, Vol. ll, No. 7,July 1950, QCI. J8, pp. [72] Inventors: John Anthony Fawcett, Thrussing- 441-443- wimam Hugh Gray, Oadby, Jacobsson, R.; Optical Properties of a Class of lnboth of England homogeneous Thin Films," Optica Acta, Vol. l0, No.

4, October, 1963, pp. 309-323. [73] Assignee: The Rank Organisation Limited,

London land Primary Examiner-David Schonberg [22] Filed: Feb. 4, 1971 Assistant ExaminerR0nald J. Stern Alt0rneyHolcombe, Wetherill & Brisebois [21] Appl. No.: 112,785

[57] ABSTRACT [30] Foreign Application Priority Data An anti-reflection multiple layer coating is formed on Feb 4 [970 Great Britain 5 397,70 a transparent substrate by successive deposition of an inner layer, at least three intermediate layers and an [52] us. Cl I l l I I i "350/164 7/33 3 outer layer, the optical thicknesses of the inner and In CL l/l'o outer layers being approximately A/4 and the overall [58] Field oriiiiIIIIIIIIIIIIIIIIIIIIIBi'i, 163-166; hwkms appmxmatey N where A is a reference wavelength within the band of 7/333 wavelengths over which reflection is to be reduced. The intermediate layers are formed with progressively [56] References cued decreasing refractive indices from the innermost to UNITED STATES PATENTS the outermost intermediate layers, either as a number of separate layers or as a single layer of graded refrac- 2,478,385 8/1949 Gaiser ..350/l64 tiveindex 3.l85,020 5/l965 Thelen 3,432,225 I 1/1968 Rock ..350/l64 24 Claims, 5 Drawing Figures MULTI-LAYER ANTI-REFLECTION COATINGS USING INTERMEDIATE LAYERS HAVING MONOTONICALLY GRADED REFRACTIVE INDEX This invention relates to anti-reflection coatings.

Anti-reflection coatings are applied to transparent substrates such as optical components with a view to reducing the reflection at the substrate surface of light of a predetermined wavelength or wavelengths.

Usually it is desired to reduce reflection from the substrate surface at more than one wavelength, for example over a band of wavelengths.

Among prior proposals are coatings comprising two and three component layers; the two layer coating comprises outer and inner layers having thicknesses of A/4 and M2 respectively, where A is a wavelength lying within a band-width over which reflection is to be reduced, while the three layer coating generally has layers of thicknesses A/4, A/2, 3A/4 respectively. However, such twoand three-layer coatings are of limited usefulness, primarily on account of the fact that the bandwidth over which low amplitude of reflection occurs is limited. Also, in the case of the three-layer coating, the overall coating thickness is such that there is a substantial risk of light absorption in the coating.

Although some three-layer coatings may in theory stantially A, where A is a reference wavelength lying within a wavelength band over which reflection is to be reduced.

The number of intermediate layers may be very large in which case they may be constituted, in effect, by a single inhomogenous compound deposit of progressively increasing refractive index.

Thus in accordance with another aspect of the invention there is provided an anti-reflection coating comprising an inner layer deposited on a transparent substrate, an outer layer, and an inhomogeneous intermediate layer having a graded refractive index which increases progressively from the outer to the inner layer, wherein the optical thicknesses of the outer and inner layers are each substantially A/4, and the overall optical thickness of the coating is substantially A, where A is a reference wavelength lying within a wavelength exhibit zero reflection at three different wavelengths at normal incidence, it is found in practice that an averaging process occurs, such that maxima and minima of reflected amplitude are smoothed out, as a result of the integration of several rays forming an image point, at different angles of incidence, as they pass through the several coated surfaces usually present in an optical system.

Also one serious consequence of the errors and tolerances which are unavoidable in the deposition of anti-reflection coatings is that the resultant spectral reflectivity characteristics may be shifted to occur over a somewhat different spectral range than that required.

As a result, higher reflectivity effects exhibited by the coating in the sidebands of the wavelength bands of minimal reflectivity, which in theory fall outside the spectral range for which the coating is designed, are brought to some extent into that range, where they impair the spectral transmission and give rise to undesirable ghost images or increased veiling glare as a result of reflection from the coating.

One of the main objects of the present invention is to provide a coating with a wide spectral range over which reflection is held to very small values, that is, with a low integrated reflection, so that the effects of manufacturing error are far less serious. These advantages are also useful when consideration is given to similar spectral shifts consequent upon variation of coating uniformity on steeply curved or large area surfaces and where there is a significant variation of angle of incidence, whether or not the coating is uniform.

According to the invention there is provided an antireflection coating comprising an inner layer 'deposited on a transparent substrate, an outer layer, and at least three intermediate layers of progressively increasing refractive index interposed successively between the outer and inner layers, wherein the optical thicknesses of the outer and inner layers are each substantially A/4, and the overall optical thickness of the coating is subband over which reflection is to be reduced.

' The coating according to the invention permits of a greater flexibility in design than previously known antireflection coatings, since the limitations imposed on the layer refractive indices are not so severe, thus allowing a greater choice from materials available in nature. Further, any given design can be used with a substrate of any refractive index likely to be met in visible light systems, by changing only the index of the layer immediately. adjacent the substrate. lt has also been found that both the layer refractive indices and thicknesses can vary from the optimum to a relatively greater extent. In conjunction with the wider bandwidth this yields coatings which have both a wider manufacturing tolerance and which can operate under the varying conditions, previously defined. Finally-the total coating thickness is reduced to one wavelength, thereby reducing the absorption risk.

Typically the said reference wavelength lies at 0 close to the harmonic mean of said wavelength band.

The outer layer should have a refractive index between 1.25 and 1.45.

In a preferred embodiment the refractive index of the inner layer is approximately equal to n," .nL where n, is the refractive index of the substrate and m is the refractive index of the outer layer. In practice, the refractive index of the inner layer lies between 0.911,. m and 1.1 H .11 inclusive.

There may be N intermediate layers, designated L,,L,, L starting from the outermost intermediate layer L immediately adjacent the outer layer L Preferably the outermost and innermost intermediate layers have respective refractive indices n and n such that:

3.5 (1.2n 1.0) +0.02NZn 2 where 5 2N 2 or 3.55(1.16n 1.00) 21 g 2.90(1.16n 1.O0)

where N 5;

N(17N) N(17-N) R 2 ("L -"1. 2W0) n,

where 5ZN 2 or (5) 0.30 2(n -n )ZO.O5 where N 5 The refractive indices of the intermediate layers are nominally valued such that the difference in refractive index between any adjacent pair of intermediate layers is substantially the same.

If the optical thickness of each layer is T then according to the above definition:

The optical thickness of both the outer and inner layers, T and TL+1 respectively, is nominally )t/4 and that for each of the intermediate layers T T is nominally A/ZN.

The refractive index values in the coating of the invention are not as critical as has been found necessary in the prior art. For example, the actual numerical spacing of the indices n to 11 inclusive of the intermediate layers need not be uniform, nor need the corresponding thicknesses T to T1,, inclusive be equal provided that n n n;, what is particularly significant is the index difference (m n A further advantageous feature is also available. Should a material having the appropriate value of n, not be available, then it is possible to use a material with an index higher or lower by a few percent, provided the range n to n; is raised and extended, or lowered and contracted, respectively. The amount is deduced empirically', the performance is still maintained.

The following equations giving values of the preferred refractive indices for the innermost and outermost intermediate layers have been deduced from theoretical studies:

1n theory any value of N 2 may be employed up to a limit set by the layer thicknesses approaching molecular dimensions (N z 250). For N 5, however, a plateau condition is reached as may be seen from equations (iii) and (iv), which are independent of N. Those knowledgeable in the art will appreciate that practical problems will be more severe as N increases. With the index change from one layer to the next decreasing, the several discrete layers may be considered as a single inhomogeneous layer, whose index grades with thickness still in accordance with the above conditions. Thus the apparent increase in practical complexity, for large values of N, in fact presents one possible method of implementing the invention in practice. For example some materials, e.g. TiO, can be evaporated under varying conditions so as to yield a graded refractive index. Alternatively, co-evaporation techniques may be employed whereby the rates of deposition from two separate sources are varied to yield the required grading.

The following examples will demonstrate the level of spectral performance of typical coatings according to this invention. These coatings are designed for the suppression of reflection over the wavelength range 380 720 n.m., being a spectral range, given the desired permissity, utilized in optical systems operative over the visible range of wavelengths, for example, 400 to 700 nm.

EXAMPLE l Refractive Optical Possible lndes Thickness Film Material Superstrate 1.0 Massive (ai Layer Lo 1.38 025A MgF, (outer) L 1.95 0.0455k L, 1.97 0.0455) L, 1.99 0.045 L, 2.01 0.0455). L. 2.03 0.055A L. 2.05 0.0455A L, 2207 0.0455A Ti0 L. 2.09 0.0455). (evaporated L, 2.11 0.0455A under varying L 2.13 0.0455A conditions) L 2.15 0.0455), L 1.66 0.25), ,0, (inner) Substrate 1.45 Massive A 495 nm EXAMPLE 2 As Example 1 except: L,, 1.86 025A Nd,0, (inner) Substrate 1.81 Massive A 495 nm Refractive Optical Possible lndex Thickness Film Material EXAMPLE 3 Superstrate 1.0 Massive (air) Layer L, 1.38 0.25). MgF, (outer) L, 2.08 00385). L, 2.10 00385), L, 2.12 0.0385k L, 2.14 0.0385k L, 2.16 0.0385), L. 2.18 0.0385). Ti0 L, 2.20 0.0385A (evaporated L, 2.22 0.0385 under varying L 2.24 0.0385k conditions) L 2.26 0.0385A L 228 0.0385), L., 2.30 0.0385k L 2.32 0.0385). L 1.75 0.25). Mg0 (inner) Substrate .52 Massive A 495 rim EXAM PLE 4 Superstrate 1.0 Massive (air) Layer L. 1.38 025A Mg!" (outer) L. 1.97 0 05561. L, 1.98 00556). L, 1.99 0.0556A L, 2.00 0 0556A Zr0, L; 2.01 0.0556A (evaporated L. 2.02 0.0556k under L, 2.03 0.05561. varying L. 2.04 0.05S6k conditions) L, 2.05 00556), L 1.66 0.25A Al,0, (inner) Substrate 1.52 Massive A 495 nm EXAMPLE 5 Superstrate 1.0 Massive (air) Layer 1., 1.38 025A MgF, (outer) L, 1.98 0.1 Cell, L, 2.05 018k Zrll, L, 2.12 018A Ti L 1.75 0.25k MgO (inner) Substrate 1.60 Massive A 495 nm 1n Example 1 the number of intermediate layers is large (N 11) and constitute in effect a single inhomogeneous layer.

The refractive index m of the outermost layer L, is 1.38 and that for the substrate is 1.45.

The refractive index of the inner (N+l) layer is obtained from the relationship: n H & n (v) Thus:

which value lies within the range:

lim -n, and 0.9 n n The intermediate layer refractive indices are obtained from equations (iii) and (iv):

and m, =3.75 1.38 3.225 1.95,

which conform to inequalities (2) and (4).

In this example A 495 nm, which value lies within the operation bandwidth of 380 720 nm.

The intermediate layers maybe regarded as a number of discrete layers of progressively different refractive index, as listed in, for example, Example 1. Alternatively, the intermediate layers may be regarded as a single inhomogeneous layerof continuously graded refractive index, spanning a total range (n;,,,,- n;,,) about a central refractive index. Thus in Example'l the intermediate layers may be expressed as a single inhomogeneous layer with a refractive index range 2.05 i010.

It may be shown that any given coating structure holds for all substrate refractive indices in the range 2.00 3 ng 3 1.40, by altering only the index nL of the innermost layer, according to the equation (v), without degrading the performance. This is demonstrated in Example 2 where the basic structure of Ex- From equation (v):

m, 1.70 actually raised theoretically to 1.75.

From equation (iii):

11,, 2.15 actually raised for practical convenience to 2.32

and equation (iv):

m 1.95 actually raised for practical convenience to 2.08.

Also the range n n is extended from 0.20 to 0.24.

Example 4 demonstrates the reverse case of Example 3 wherein the graded refractive index range is lowered and narrowed and m has been suitably decreased.

In this particular case the range n n,,, is decreased from 0.20 to 0.08, an amount greater than the overall lowering of the range, the center of which is decreased from 2.05 to 2.01, so that the actual nL, value is in fact slightly increased. All the values fall, however, within the ranges given by inequalities (2),

Example 5 shows an application, with N 3, where the intermediate layers are individual separate layers. Also that the thicknesses of these intermediate layers can be varied from being nominally equal with negligible effect on performance.

The index uniformity can be similarly varied without loss of performance, that is to say, the refractive index step between the adjoining intermediate layers can depart from strict equality for all adjoining intermediate layers without loss of performance.

The accompanying drawings illustrate, purely diagrammatically, multi-layer anti-reflection coatings according to the invention in enlarged cross-section, not to scale. FlGS. l S are respectively cross-sectional representations of the coatings described in Examples 1 5.

1n all the Figures, the same reference letters are used to designate corresponding components. Thus the substrate is denoted by S, and the various layers by L, with suffixed numerals corresponding to the layer notation used in Examples 1 5, the outermost layer in each case being designated L,,.

What is claimed is:

1. An anti-reflection coating on a transparent substrate, said coating comprising an inner layer closest to said substrate, an outer layer farthest from said substrate, and at least three intermediate layers of progressively increasing refractive index interposed successively between the outer and inner layers, the optical thicknesses of the outer and inner layers being each substantially M4, and the overall optical thickness of the coating being substantially A, where k is a reference wavelength lying within a wavelength band over which reflection is to be reduced.

2. A coating according to claim 1, wherein said reference wavelength lies at or close to the harmonic mean of said wavelength band.

3. A coating according to claim 1, wherein the outer layer has a refractive index between 1.25 and 1.45.

4. A coating according to claim 1, wherein the difference between the refractive indices of any two adjacent intermediate layers is substantially the same.

5. A coating according to claim 1, wherein the refractive index of the inner layer is approximately equal to.n,"'- m where n, is the refractive index of the substrate and 111,, is the refractive index of the outer layer.

6. A coating according to claim 5, wherein the refractive index of the inner layer lies between 0.9 n, -n;,,, and 1.1 01,". nb inclusive.

7. An anti-reflection coating on a transparent substrate, said coating comprising an inner layer closest to said substrate, an outer layer farthest from said substrate, and an inhomogeneous intermediate layer having a graded refractive index which increases progressively from the outer to the inner layer, the optical thicknesses of the outer and inner layers being each substantially M4, and the overall optical thickness of the coating being substantially A, where )1 is a reference wavelength lying within a wavelength band over which reflection is to be reduced.

8. A coating according to claim 7, in which said substrate has a refractive index between 1.40 and 2.00.

9. A coating according to claim 7, wherein the said reference wavelength is at least approximately equal to the harmonic mean of said wavelength band.

10. A coating according to claim 7, wherein the outer layer has a refractive index between 1.25 and 1.45.

11. A coating according to claim 7, wherein the refractive index of the inner layer is approximately equal to n 'n where n, is the refractive index of the substrate and 111. is the refractive index of the outer layer.

12. An anti-reflection coating on a transparent substrate, said coating comprising an inner layer closest to said substrate, an outer layer farthest from said substrate, and a number N of at least three and less than six intermediate layers designated L,, L L starting from the outermost intermediate layer L immediately adjacent the outer layer L the successive intermediate layers between the outer and inner layers having progressively increasing refractive indices n m n and the outer layer having a refractive index 111, such that:

the outer and inner layers each having a thickness of substantially A /4 and the coating having an overall thickness of substantially k, where k is a reference wavelength lying within a wavelength band over which reflection is to be reduced.

increasing refractive indices n n nL and the outer layer having a refractive index 11 such that:

8 3.55(1.16n;, 1.00) n 2.90(1.16n 1.00) 4 0.30 (n n 0.05 6 14. A coating according to claim 12, wherein the refractive index a of the outer layer is between 1.25 and 1.45.

15. A coating according to claim 13, wherein the refractive index m of the outer layer is between 1.25 and 1.45.

16. A coating according to claim 12, wherein the refractive index of the inner layer lies between 0.9 ng" "'n and 1.1 ng ""n inclusive.

17. A coating according to claim 13, wherein the refractive index of the inner layer lies between 0.9 ng" "-11 and 1.1 ng -m, inclusive.

18. A coating according to claim 12, wherein said substrate has a refractive index between 1.40 and 2.00.

19. A coating according to claim 13, wherein said substrate has a refractive index between 1.40 and 2.00.

20. An anti-reflection coating according to claim 13, wherein the outer layer has refractive index 11 of 1.38

and there are eleven intermediate layers L, to L with refractive indices 11 to 11 as follows:

each intermediate layer having a thickness of 0.0455)- (A 495nm), and wherein the inner layer has a refractive index of 1.66, and said substrate has a refractive index of 1.45.

21. An anti-reflection coating according to claim 13, wherein the outerlayer has a refractive index n1, of

1.38 and there are eleven intermediate layers L to L, with refractive indices 11 to m. as follows:

each intermediate layer having a thickness of 0.0455 A A 495nm), and wherein the inner layer has a refractive index of 1.86 and said substrate has a refractive index of 1.81.

22. An anti-reflection coating according to claim 13, wherein the outer layer has a refractive index m of 1.38 and there are thirteen intermediate layers L to L, with refractive indices m to m as follows:

nrs =2.22

each intermediate layer having a thickness of 0.0385). ()t= 495nm) and wherein the inner layer has arefractive index of 1.75, and said substrate has a refractive index of 1.52.

23. Ananti-reflection coating according to claim 13, wherein the outer layer has a refractive index m of 1.38 and there are nine intermediate layers L, to L with refractive indices m, to n as follows:

the first intermediate layer L having a thickness of 0.14)\ (1\ 495nm) and the other two intermediate layers L, and L having equal thicknesses of 0. 1 8A, and

wherein the inner layer has a refractive index 1.75, the

coating being applied to a substrate of refractive index i t 1 i 

2. A coating according to claim 1, wherein said reference wavelength lies at or close to the harmonic mean of said wavelength band.
 3. A coating according to claim 1, wherein the outer layer has a refractive index between 1.25 and 1.45.
 4. A coating according to claim 1, wherEin the difference between the refractive indices of any two adjacent intermediate layers is substantially the same.
 5. A coating according to claim 1, wherein the refractive index of the inner layer is approximately equal to ng1/2 .nL , where ng is the refractive index of the substrate and nL is the refractive index of the outer layer.
 6. A coating according to claim 5, wherein the refractive index of the inner layer lies between 0.9 ng1/2 .nL and 1.1 ng1/2.nL inclusive.
 7. An anti-reflection coating on a transparent substrate, said coating comprising an inner layer closest to said substrate, an outer layer farthest from said substrate, and an inhomogeneous intermediate layer having a graded refractive index which increases progressively from the outer to the inner layer, the optical thicknesses of the outer and inner layers being each substantially lambda /4, and the overall optical thickness of the coating being substantially lambda , where lambda is a reference wavelength lying within a wavelength band over which reflection is to be reduced.
 8. A coating according to claim 7, in which said substrate has a refractive index between 1.40 and 2.00.
 9. A coating according to claim 7, wherein the said reference wavelength is at least approximately equal to the harmonic mean of said wavelength band.
 10. A coating according to claim 7, wherein the outer layer has a refractive index between 1.25 and 1.45.
 11. A coating according to claim 7, wherein the refractive index of the inner layer is approximately equal to ng1/2.nL , where ng is the refractive index of the substrate and nL is the refractive index of the outer layer.
 12. An anti-reflection coating on a transparent substrate, said coating comprising an inner layer closest to said substrate, an outer layer farthest from said substrate, and a number N of at least three and less than six intermediate layers designated L1, L2 . . . LN, starting from the outermost intermediate layer L1 immediately adjacent the outer layer Lo, the successive intermediate layers between the outer and inner layers having progressively increasing refractive indices nL , nL , . . . , nL and the outer layer having a refractive index nL , such that:
 13. An anti-reflection coating on a transparent substrate, said coating comprising an inner layer closest to said substrate, an outer layer farthest from said substrate and a number N greater than five intermediate layers designated L1, L2 . . . LN, starting from the outermost intermediate layer L1 immediately adjacent the outer layer Lo, the successive intermediate layers between the outer and inner layers having progressively increasing refractive indices nL , nL , . . . , nL and the outer layer having a refractive index nL , such that: 3.33(1.24nL -1.00)>nL >2.72(1.24nL - 1.00) (2) 3.55(1.16nL - 1.00)>nL >2.90(1.16nL - 1.00)(4)0.30>(nL -nL )>0.05 (6)
 14. A coating according to claim 12, wherein the refractive index nL of the outer layer is between 1.25 and 1.45.
 15. A coating according to claim 13, wherein the refractive inDex nL of the outer layer is between 1.25 and 1.45.
 16. A coating according to claim 12, wherein the refractive index of the inner layer lies between 0.9 ng1/2.nL and 1.1 ng 1/2.nL inclusive.
 17. A coating according to claim 13, wherein the refractive index of the inner layer lies between 0.9 ng1/2.nL and 1.1 ng1/2.nL inclusive.
 18. A coating according to claim 12, wherein said substrate has a refractive index between 1.40 and 2.00.
 19. A coating according to claim 13, wherein said substrate has a refractive index between 1.40 and 2.00.
 20. An anti-reflection coating according to claim 13, wherein the outer layer has refractive index nL of 1.38 and there are eleven intermediate layers L1 to L11 with refractive indices nL to nL as follows: nL 1.95 nL 1.97 nL 1.99 nL 2.01 nL 2.03 nL 2.05 nL 2.07 nL 2.09 nL 2.11 nL 2.13 nL 2.15 each intermediate layer having a thickness of 0.0455 lambda ( lambda 495nm), and wherein the inner layer has a refractive index of 1.66, and said substrate has a refractive index of 1.45.
 21. An anti-reflection coating according to claim 13, wherein the outerlayer has a refractive index nL of 1.38 and there are eleven intermediate layers L1 to L11 with refractive indices nL to nL as follows: nL 1.95 nL 1.97 nL 1.99 nL 2.01 nL 2.03 nL 2.05 nL 2.07 nL 2.09 nL 2.11 nL 2.13 nL 2.15 each intermediate layer having a thickness of 0.0455 lambda ( lambda 495nm), and wherein the inner layer has a refractive index of 1.86 and said substrate has a refractive index of 1.81.
 22. An anti-reflection coating according to claim 13, wherein the outer layer has a refractive index nL of 1.38 and there are thirteen intermediate layers L1 to L13 with refractive indices nL to nL as follows: nL 2.08 nL 2.10nL 2.12 nL 2.14 nL 2.16 nL 2.18 nL 2.20 nL 2.22 nL 2.24 nL 2.26 nL 2.28 nL 2.30 nL 2.32 each intermediate layer having a thickness of 0.0385 lambda ( lambda 495nm) and wherein the inner layer has a refractive index of 1.75, and said substrate has a refractive index of 1.52.
 23. An anti-reflection coating according to claim 13, wherein the outer layer has a refractive index nL of 1.38 and there are nine intermediate layers L1 to L9 with refractive indices nL to nL as follows: nL 1.97 nL 1.98 nL 1.99 nL 2.00 nL 2.01 nL 2.02 nL 2.03 nL 2.04 nL 2.05 each intermediate layer having a thickness of 0.0556 lambda ( lambda 495nm) and wherein the inner layer has a refractive index of 1.66, and said substrate has a refractive index of 1.52.
 24. An anti-reflection coating according to claim 12, wherein the outer layer has a refractive index nL of 1.38 and there are three intermediate layers 1L1 to L3 with refractive indices nL to nL as follows: nL 1.98 nL 2.05 nL 2.12 the first intermediate layer L1 having a thickness of 0.14 lambda ( lambda 495nm) and the other two intermediate layers L2 and L3 having equal thicknesses of 0.18 lambda , and wherein the inner layer has a refractive index 1.75, the coating being applied to a substrate of refractive index 1.60. 